Addition and Subtraction of Fractions - AWS
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Module 3 Addition and Subtraction of Fractions
Name _________________________ Class Code __________
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Topic A: Equivalent Fractions Lesson 1 Lesson 2 Topic AB: Representing Fractions in Different Forms Lesson AB 1 Improper Fractions to Mixed Numbers Lesson AB 2 Reducing Fractions Lesson AB 3 Comparing Fractions Topic B: Making Like Units Pictorially Lesson 3 Lesson 4 Lesson 5 Lesson 5A Mixed Numbers to Improper Fractions Lesson 6 Lesson 7
Topic C: Making Like Units Numerically Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12
Topic D: Further Applications Lesson 13 Lesson 14 Lesson 15 Lesson 16 Word Problems
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Module 3 – Introduction and Review Fractions with Number Lines Review What is a fraction ______________________________________________ _____________________________________________________________ What are the parts of a fraction?
5 6 What do the parts of the fraction tell us? Numerator _______________________________________________ Denominator ______________________________________________
Examples of Fractions :
______________________________________________ ______________________________________________ ______________________________________________ ______________________________________________ ______________________________________________ ______________________________________________ Draw
1 3
4 5
6 8
4
Plotting Fractions on number lines
If the numerator is less than the denominator the fraction is less than 1.
1 3
4 3
Add the numerator to make each fraction equal to 1 3
=1
Plot
3 6
2 Plot 5
6
=1
2
=1
8
=1
16
=1
5
6 Plot 8
Plot
1 4
Plot
2 5
Plot 1
2 5
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Module 3 – Lesson 1 Equivalent Fractions with Number Lines Application Problem 15 kilograms of rice are separated equally into 4 containers. How many kilograms of rice are in each container? Express your answer as a decimal and as a fraction.
Simplify or Solve 3x4+6÷2
3 x (4 + 6) ÷ 2
207 x 124
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Equivalent Fractions On the number line plot
1 2
and
3 6
1 2
3 6
On the number line plot
1 3
and
2 6
1 3
1 1 x = 3 3 x
2 6
=
2 6
How can you make an equivalent fraction?
____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________
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Problem Set Make Equivalent fractions for the fractions below and plot them on a number line.
1 1 x = 4 4 x
=
2 2 x = 3 3 x
=
Using the same process make equivalent fractions for the fractions below.
4 7
1 8
2 5
7 9
9 10
3 7
1 14
9 11
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Homework Make Equivalent fractions for the fractions below and plot them on a number line.
3 3 x = 4 4 x
=
1 1 x = 3 3 x
=
Using the same process make equivalent fractions for the fractions below.
4 5
1 8
2 5
7 9
9 10
3 7
1 14
9 11
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Lesson 2 Equivalent Fractions with the Sums of Fractions with Like Denominators Application Problem Mr. Hopkins has a 1 meter wire he is using to make clocks. Each fourth meter is marked off with 5 smaller equal lengths. If Mr. Hopkins bends the wire at
¾ meter, what fraction of the marks is that?
Try solving using a number line or a tape diagram
Write in standard form and solve Three times the difference between 6 seventeens and 4 twenty fours
Solve
2.34 x 17 =
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On the number line, mark the end points as zero and 1. Between zero and 1 estimate to make three parts of equal length and label them with their fractional value.
On your number line, show one third plus on third with arrows designating lengths.
The answer is
Express this as a multiplication equation and as an addition sentence.
Following the same pattern of adding unit fractions by joining lengths, show 3 fourths on a new number line. (Add two fractions to equal ¾)
Write the addition sentence.
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On a number line, again mark the end points as zero and one. Between zero and one, estimate to make 8 parts of equal length. This time only label what is necessary to show 3 eighths. Represent 3 eighths + 3 eighths + 1 eighth on your number line. The answer is Express this as a multiplication equation and as an addition equation. On a number line, mark the end points as 0 halves and 6 halves below the number line. Estimate to make 6 parts of equal length. This time only label 2 halves. Record the whole number equivalents above the line. Represent 3 x 2 halves on your number line. The answer is Express this as an addition equation and as an multiplication equation.
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Use a number line. Mark the end points as 0 fifths and 10 fifths below it. Estimate and give a value to the halfway point. What will be the value of the halfway point? Make 10 parts of equal length from 0 fifths to 10 fifths. Record the whole number equivalents above the line. Label 8 fifths on your number line. Show 8 fifths as the sum of 5 fifths and 3 fifths on your number line. Express this as an addition equation in two ways: as the sum of fifths and as the sum of a whole number and fifths. 8 fifths is between what 2 whole numbers?
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Use a number line. Mark the end points as 0 thirds and 9 thirds below the number line. Divide the whole length into three equal smaller lengths and mark their values using thirds. What are the values of those points? Mark the whole number equivalents above the line. Divide each of those whole number lengths into three smaller lengths. Mark the number 7 thirds. Show 7 thirds as two units of 3 thirds and one more third on your number line and in an equation. 7 thirds is between what two whole numbers?
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Express each fraction as the sum of two or three equal fractional parts. Rewrite each as a multiplication equation.
6 8
6 2 2 2 8 = 8 +8 +8
=
3 3 + 8 8
12 14
15 20
or
9 10
3 4
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Lesson 2 Problem Set 1. Show each expression on a number line. Solve. a)
c)
b)
d)
x
2) Express each fraction as the sum of two or three equal fractional parts. Rewrite each as a multiplication equation.
6 a)
c)
9
b)
12 10
d)
7
2
27 5
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3) Express each of the following as the sum of a whole number and a fraction.
4) Marisela cut four equivalent lengths of ribbon. Each was 5 eighths of a yard long. How many yards of fabric did she cut? Express your answer as the sum of a whole number and the remaining fractional units. Draw a number line to represent the problem.
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Lesson 2 Homework 1) Show each expression on a number line. Solve. 1)
x
2) Express each fraction as the sum of two or three equal fractional parts. Rewrite each as a multiplication equation. a) b)
19 c)
d)
3) Express each of the following as the sum of a whole number and a fraction. a) b)
c)
d)
4) Natalie sawed five boards of equal length to make a stool. Each was 9 tenths of a meter long. How many meters of board did she saw? Express your answer as the sum of a whole number and the remaining fractional units. Draw a number line to represent the problem.
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Improper Fractions to Mixed Numbers
Divide into fifths and plot
Plot
17 now write it as a whole number and a fraction 5
10 then write it as a whole number and a fraction 4
Converting improper fractions to mixed numbers strategy.
17 5 First divide the numerator by the denominator
3
3
The 3 is your whole number. While the remainder becomes the numerator.
Your denominator stays the same. Here is your mixed number
17 ÷ 5 = 3 r 2
17 2
13 2
79 9
21
35 4
37 5
13 7
5 2
28 3
25 3
65 7
32 6
36 5
64 7
12 7
42 5
22
78 9
66 7
68 8
3 2
19 3
38 4
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Improper Fractions to Mixed Numbers Homework
17 5 First divide the numerator by the denominator
3
3
The 3 is your whole number. While the remainder becomes the numerator.
Your denominator stays the same. Here is your mixed number
17 ÷ 5 = 3 r 2
37 5
61 7
48 7
32 5
55 7
18 4
13 2
19 2
24 9
24
55 6
8 7
9 4
5 3
17 4
42 4
13 3
74 8
11 2
52 7
16 3
39 8
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Divisibility Rules 2 – A number is divisible by 2 if it is even 3 – A number is divisible by 3 if the sum of its digits is divisible by 3 Example – 93 9 + 3 = 12 12 is divisible by 3 so 93 is divisible by 3 4 – A number is divisible by 4 if the last 2 digits are divisible by 4 Example – 724 24 is divisible by 4 so 724 is divisible by 4 5 – A number is divisible by 5 if it ends in a 5 or a 0 6 – A number is divisible by 6 if it is divisible by both 2 and 3 10 – A number is divisible by 10 if it ends in a 0 Reducing Fractions Greatest Common Factor
12
and 18
8
and
16
26
10
and
30
6
and
15
Find the greatest common factor of the numerator and the denominator
3 9
14 21
4 8
Use the Greatest common factor to reduce Each Fraction as Much as Possible
9 3 = 3 12
X X
3 3 = 4 4
Or
27
10 40
8 64
40 64
50 60
18 27
3 24
8 12
30 80
8 48
40 48
16 24
24 32
21 28
21 56
9 36
35 42
6 48
20 30
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Reducing Fractions Homework Reduce Each Fraction as Much as Possible
5 40
4 16
5 20
6 9
2 4
2 16
24 32
3 6
8 12
15 24
21 56
10 60
49 56
7 56
3 12
5 15
9 72
15 18
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Least Common Multiple and Comparing Fractions
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Comparing Fractions
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Comparing fractions on number lines Plot one fraction on each Number line and then compare.
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Cross multiplying to compare
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Problem Set
34
35
36
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Lesson 3 Adding Fractions with Unlike Units by Making Equal Fractions Application Problem Alex squeezed 2 liters of juice for breakfast. If he pours the juice equally into 5 glasses, how many liters of juice will be in each glass? (Bonus: How many milliliters are in each glass?)
Solve – Use Decimals 216 ÷ 90 =
643 ÷ 80 =
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Adding Fractions
2 4 8 + 8 =
What has to be the same in order to add two fractions? _____________________
4 8
+
1 8
=
1 6
+
4 6
=
How can you add two fractions with different denominators? ???? 1 4 + 8 6 Can we change a denominator in a fraction??? When???? Can we find an equivalent fraction for 4/8 and 1/6 that both fractions have the same denominator? Find the Least Common Multiple for 8 and 6 to help you find equivalent fractions with common denominators. Least Common Multiples 8 6 8 16 24 32 40 48 6 12 18 24 30 36 42 48 Which is the lowest one they have in common? There’s the denominator to use!!!
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Make and equivalent fraction for 4/8 and 1/6 so both fractions have 24 as a denominator. 1 4 6 8 How to make equivalent fractions reminder Now you can add the fractions
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Adding fractions Step 1 – rewrite vertically Step 2 – find the least common multiple for both denominators Step 3 – make an equivalent fractions using the new common denominator Step 4 – add the numerators
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Adding fractions Step 1 – rewrite vertically Step 2 – find the least common multiple for both denominators Step 3 – make an equivalent fractions using the new common denominator Step 4 – add the numerators
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Lesson 3 Problem Set 1) For the following problems, find common denominators and solve – simplify your answers.
a..
b.
c. d.
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e. f.
Solve the following problems. Draw a picture and/or write the number sentence that proves the answer. Simplify your answer. Jamal used 1/3 yard of ribbon to tie a package and 1/6 yard of ribbon to tie a bow. How many yards of ribbon did Jamal use?
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Over the weekend, Nolan drank 1/6 quart of orange juice, and Andrea drank 3/4 quart of orange juice. How many quarts did they drink together? Nadia spent 1/4 of her money on a shirt and 2/5 of her money on new shoes. What fraction of Nadia’s money has been spent? What fraction of her money is left?
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Lesson 3 Homework 1) For the following problems, draw a picture using the rectangular fraction model and write the answer. Simplify your answer. a)
b)
c)
d)
45 e)
f)
Solve the following problems. Draw a picture and/or write the number sentence that proves the answer. Rajesh jogged 3/4 mile, and then walked 1/6 mile to cool down. How far did he travel?
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Cynthia completed 2/3 of the items on her to‐do list in the morning, and finished
1/8 of the items during her lunch break. How much of her to‐do list is finished by the end of her lunch break? (Bonus: How much of her to‐do list does she still have to do after lunch?) Sam read 2/5 of her book over the weekend, and 1/6 of it on Monday. What fraction of the book has she read? What fraction of the book is left?
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Lesson 4 Add Fractions with Sums Between 1 and 2 Application Problem Leslie has 1 liter of milk in her fridge to drink today. She drank 1/2 liter of milk for breakfast and 2/5 liter of milk for dinner. How many liters did Leslie drink during breakfast and dinner?
(Bonus: How much milk does Leslie have left over to go with her dessert, a brownie? Give your answer as a fraction of liters and as a decimal.)
Simplify 183 – 3 x 50 – (2 + 6)
[56 ÷ (11 – 3)] + 3 3
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1 1 When you see this problem, can you estimate the answer? 3 4 Will it be more or less than 1? Now look at this problem. Estimate the answer. 1 3 4 2 Will it be more or less than 1? What stops us from simply adding?
Find common denominators and then writing the new equation.
What is unusual about the answer?
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Solve
4 + 1 5 2
Solve
2 + 3 3 5
Solve
3 + 2 8 3
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Lesson 4 Problem Set For the following problems, find common denominators and write the answer. When possible, write your answer as a mixed number. a. b.
c.
d.
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e.
f.
Solve the following problems. Draw a picture and/or write the number sentence that proves the answer. Simplify your answer. Penny used 2/5 lb of flour to bake a vanilla cake. She used another 3/4 lb of flour to bake a chocolate cake. How much flour did she use altogether?
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Carlos wants to practice piano 2 hours each day. He practices piano for 3/4 hour before school and 7/10 hour when he gets home. How many hours has Carlos practiced piano? How much longer does he need to practice before going to bed in order to meet his goal?
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Lesson 4 Homework Directions: For the following problems, draw a picture using the rectangular fraction model and write the answer. When possible, write your answer as a mixed number. a. b.
c.
d.
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e.
f.
Solve the following problems. Draw a picture and/or write the number sentence that proves the answer. Simplify your answer. Sam made 2/3 liter of punch and 3/4 liter of tea to take to a party. How many liters of beverages did Sam bring to the party?
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Mr. Sinofsky used 5/8 of a tank of gas on a trip to visit relatives for the weekend and another half of a tank commuting to work the next week. He then took another weekend trip and used 1/4 tank of gas. How many tanks of gas did Mr. Sinofsky use altogether?
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Lesson 5 Subtract Fractions with Unlike Units by Using Equivalent Fractions Application Problem A farmer uses 3/4 of his field to plant corn, 1/6 of his field to plant beans , and the rest to plant wheat. What fraction of his field is used for wheat?
Estimate and then solve for actually amount 2307 x 452
782 x 122
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Can we subtract this? Explain.
3 - 2 = 5 5
Can we subtract this? Explain.
1 - 1 = 3 4
1 - 1 = 2 5
2 - 1 = 3 4
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1 - 2 = 2 7
4 - 2 = 5 3
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Lesson 5 Problem Set For the following problems, find common denominators and write the answer. Simplify your answer. a. b.
c.
d.
60
e.
f.
Mr. Penman had 2/3 liter of salt water. He used 1/5 of a liter for an experiment. How much salt water does Mr. Penman have left?
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Sandra says that because all you have to do is subtract the numerators and subtract the denominators. Convince Sandra that she is wrong. You may draw a rectangular fraction model to help.
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Lesson 5 Homework 1) Find common denominator and subtract.
2) Find the difference. Convert to fractions with common denominators. a.
b.
c.
d.
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e.
f.
Robin used 1/4 pound of butter to make a cake. Afterward she had 5/8 of a pound left. How much butter did she have at first?
Katrina needs 3/5 kilogram of flour for a recipe. Her mother has 3/7 kilogram in her pantry. Is this enough flour to make the recipe If not, how much more will she need?
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Mixed Numbers to Improper Fractions
2 1/6 0
Plot on the number line
1
How many 6ths all together?
2
3
2
3
2
3
_____
6 1 5/8 0
Plot on the number line
1
How many 8ths all together?
_____
8 2 2/4 0
Plot on the number line
1
How many 4ths all together?
_____
4
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Strategy First multiply the denominator times the whole number.
1
2 /6 6 × 2 = 12 Next, add your answer from step 1 to your numerator. 12 + 1 = 13 Keep your denominator the same 13 6 _____________________________________________________________
1 5/8
2 2/4
denominator x whole number Add answer to the numerator Keep denominator the same
2 6
1 7
2 5
66
1 8
1 6
4 6
4 6
6 7
2 5
2 10
1 9
1 3
67
4 6
1 2
2 4
2 8
2 3
1 7
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Mixed Numbers to Improper Fractions Homework
Mixed Numbers to Improper Fractions
2 5
First multiply the denominator times the whole number. 5 × 3 = 15 Next, add your answer from step 1 to your numerator. 15 + 2 = 17 Keep your denominator the same
17 5 _____________________________________________________________
1 4
6 9
5 8
5 8
6 7
1 2
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4 8
4 6
3 10
8 9
8 9
6 9
1 4
1 2
8 9
4 6
5 6
6 9
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Lesson 6 – Subtract Fractions from numbers between 1 and 2 Application Problem The Napoli family combined two bags of dry cat food in a plastic container. One bag had 5/6 kg. The other bag had 3/4 kg. What was the total weight of the container after the bags were combined?
Solve 104.35 x 34 =
480,000 ÷ 600 =
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- Convert mixed number to improper fraction - Find common denominator - Solve - Simplify
1 1 1 3 2
1 1 1 5 3
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3 4 1 4 5
4 1 1 9 2
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Lesson 6 Problem Set
Convert mixed number to improper fraction - Find common denominator – Solve - Simplify a.
b.
c.
d.
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e.
f.
1. Jean‐Luc jogged around the lake in 1 1/4 hour. William jogged the same distance in 5/6 hour. How much longer did Jean‐Luc take than William in hours? How many more minutes? 2. Is it true that ? Prove your answer.
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Lesson 6 Homework 1.
a.
Find the difference. Use a rectangular fraction model to show how to convert to fractions with common denominators. b.
c.
d.
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e.
f.
g.
h.
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2.
Sam had 1 1/2 m of rope. He cut off 5/8 m and used it for a project. How much rope does Sam have left?
3.
Jackson had 1 3/8 kg of fertilizer. He used some to fertilize a flower bed and he only had 2/3 kg left. How much fertilizer was used in the flower bed?
78
Lesson 7 – Two Step Word Problems Lesson 7 Problem Set George weeded 1/5 of the garden, and Summer weeded some, too. When they were finished, 2/3 of the garden still needed to be weeded. What fraction of the garden did Summer weed?
Jing spent 1/3 of her money on a pack of pens, 1/2 of her money on a pack of markers, and 1/8 of her money on a pack of pencils. What fraction of her money is left?
79
Shelby bought a 2 ounce tube of blue paint. She used 2/3 ounce to paint the water, 3/5 ounce to paint the sky, and some to paint a flag. After that she has 2/15 ounce left. How much paint did Shelby use to paint her flag?
Jim sold 3/4 gallon of lemonade. Dwight sold some lemonade too.
Together, they sold 1 5/12 gallons. Who sold more lemonade, Jim or Dwight? How much more?
Leonard spent 1/4 of his money on a sandwich. He spent 2 times as much on a gift for his brother as on some comic books. He had 3/8 of his money left. What fraction of his money did he spend on the comic books?
80
Lesson 7 Homework Christine baked a pumpkin pie. She ate 1/6 of the pie. Her brother ate 1/3 of it, and gave the left overs to his friends. What fraction of the pie did he give to his friends?
Liang went to the bookstore. He spent 1/3 of his money on a pen and 4/7 of it on books. What fraction of his money did he have left?
Tiffany bought 2/5 kg of cherries. Linda bought 1/10 kg of cherries less than Tiffany. How many kg of cherries did they buy altogether?
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Mr. Rivas bought a can of paint. He used 3/8 of it to paint a book shelf. He used 1/4 of it to paint a wagon. He used some of it to paint a bird house, and have 1/8 of paint left. How much paint did he use for the bird house?
Ribbon A is 1/3 m long. It is 2/5 m shorter than ribbon B. What’s the total length of two ribbons?
82
Fraction Practice In order to Add, Subtract, or compare fractions what do they have to have? ____________________________________________________ What is a fraction that has a larger numerator than denominator called? ____________________________________________________ A whole number that is followed by a fraction is called? _____________________ Make an equivalent fraction Make each fraction equal 1 4 =1 =1 7 8 16 Express each fraction as the sum of 1 two or three equal fractional parts. 8 Rewrite each as a multiplication equation. 2 6 2 2 2 3 3 6 = + or = + + 5 8 8 8 8 8 8 8 7 12 9 15 Convert to improper fractions
8 10 4 6
1 5
1 6
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Convert to mixed numbers
32 5
55 7
18 4
Reduce
40 48
16 24
24 32
84
Lessons 9 and 10 – Adding and Subtracting Fractions Application Problem Hannah and her friend are training to run in a 2 mile race. On Monday, Hannah runs 1/2 mile. On Tuesday, she runs 1/5 mile further than she ran on Monday. How far did Hannah run on Tuesday?
If her friend ran 3/4 mile on Tuesday, how many miles did the girls run in all on Tuesday?
85
Sam and Nathan are training for a race. Monday, Sam ran 2 3/4 miles, and Nathan ran 2 1/3 miles. How much farther did Sam run than Nathan?
86
Lessons 9 and 10 Problem Set Solve and Simplify
87
88
89
Whitney says that to add fractions with different denominators, you always have to multiply the denominators to find the common unit, for example: Show Whitney how she could have chosen a denominator smaller than 24, and solve the problem. Jackie brought of a gallon of iced tea to the party. Bill brought of a gallon of iced tea to the same party. How much iced tea did Jackie and Bill bring to the party?
90
Madame Curie made some radium in her lab. She used kg of the radium in an experiment and had kg left. How much radium did she have at first? (Bonus: If she performed the experiment twice, how much radium would she have left?)
Erin jogged miles on Monday. Wednesday she jogged miles, and on Friday she jogged miles. How far did Erin jog altogether?
91
Darren bought some paint. He used gallons painting his living room. After that, he had gallons left. How much paint did he buy? Clayton says that will be more than 5 but less than 6 since 2 + 3 is 5. Is Clayton’s reasoning correct? Prove him right or wrong.
92
Lessons 9 and 10 Homework Make like units, then add. Use an equation to show your thinking.
93
Add.
94
95
On Monday, Ka practices guitar for 2/3 of one hour. When she’s finished, she practices piano for ¾ of one hour. How much time did Ka spend practicing instruments on Monday?
96
Ms. How buys a bag of rice to cook dinner. She used 3/5 kg of rice and still had 2 and ¼ kg left. How heavy was the bag of rice that Ms. How bought?
Joe spends 2/5 of his money on a jacket and 3/8 of his money on a shirt. He spends the rest on a pair of pants. What fraction of his money does he use to buy the pants?
97
Angela practiced piano for 2 ½ hours on Friday, 2 1/3 hours on Saturday, and 3 2/3 hours on Sunday. How much time did Angela practice piano during the weekend?
String A is 3 5 /6 meters long. String B is 2 1/ 4 long. What’s the total length of both strings?
98
Lessons 11 and 12 Adding and Subtracting Fractions Application Problem Meredith went to the movies. She spent 2/5 of her money on a ticket and 3/7 of her money on popcorn. How much of her money did she spend? (Bonus: How much of her money is left?) Max’s reading assignment was to read 15 1/2 pages. After reading 4 1/3 pages, he took a break. How many more pages does he need to read to finish his assignment?
99
To make punch for the class party, Mrs. Lui mixed 1 1/3 cups orange juice, 3/4 cup apple juice, 2/3 cup cranberry juice, and 3/4 cup lemonlime soda. Mixed together, how many cups of punch does the recipe make? (Bonus: Each student drinks 1 cup. How many recipes does Mrs. Lui need to serve her 20 students?)
100
101
Lessons 11 and 12 Problem Set Generate equivalent fractions to get the same unit, then subtract.
102
103
Subtract.
104
George says that to subtract fractions with different denominators, you always have to multiply the denominators to find the common unit, for example: Show George how he could have chosen a denominator smaller than 48, and solve the problem.
Meiling has liter of orange juice. She drinks liter. How much orange juice does she have left? (Bonus: If her brother then drinks twice as much as Meiling, how much is left?)
105
Harlan used
kg of sand to make a large hourglass. To make a small hourglass
he only used kg of sand. How much more sand does it take to make the large hourglass than the small one? Toby wrote the following: Is Toby’s calculation correct? Draw a diagram to support your answer.
106
Mr. Neville Iceguy mixed up gallons of chili for a party. If gallons of chili was mild, and the rest was extra spicy, how much extra spicy chili did Mr. N. Iceguy make? Jazmyne determined to spent
hours studying over the weekend. She spent
hours studying on Friday evening and
hours on Saturday. How much
longer does she need to spend studying on Sunday in order to reach her goal?
107
Lessons 11 and 12 Homework First find a common unit, then subtract.
108
109
Subtract.
110
111
Sandy ate of a candy bar. John ate of it. How much more of the candy bar did John eat than Sandy? yards of cloth are needed to make a woman’s dress. yards of cloth are needed to make a girl’s dress. How much more cloth is needed to make a woman’s dress than a girl’s dress?
112
Bill reads of a book on Monday. He reads of the book on Tuesday. If he finishes reading the book on Wednesday, what fraction of the book did he read on Wednesday? Tank A has a capacity of 9.5 gallons. gallons of the tank’s water are poured out. How much water is left in the tank?
113
Tony wrote the following: Is Tony’s statement correct? Explain. Ms. Sanger blended there were she use?
gallons of iced tea with some lemonade for a picnic. If gallons in the mixture, how many gallons of lemonade did
114
A carpenter has a
foot wood plank. He cuts off
feet to replace the slat
of a deck and feet to repair a bannister. He uses the rest of the plank to fix a stair. How many feet of wood does the carpenter use to fix the stair?
115
Lesson 13 – Fraction Benchmarks to Check Reasonableness Application Problem Mark jogged 3 5/7 km. His sister jogged 2 4/5 km. How much farther did Mark jog than his sister?
Solve: 62 x 100 =
282 x 42 =
26.72 x 100 =
240 x 2000 =
116
1 + 3 2 4 Without calculating what can you tell me about the value of this expression?
2 2 1 5 ‐ 3 Without calculating what can you tell me about the value of this expression?
4 10
+
1 3
Without calculating what can you tell me about the value of this expression?
4 10
+
2 9
Without calculating what can you tell me about the value of this expression?
117
4 9 1 7 ‐ 10 Without calculating what can you tell me about the value of this expression?
4 5
-
1 8
Without calculating what can you tell me about the value of this expression?
Use > , , ,
Module 3 Addition and Subtraction of Fractions
Name _________________________ Class Code __________
2
Topic A: Equivalent Fractions Lesson 1 Lesson 2 Topic AB: Representing Fractions in Different Forms Lesson AB 1 Improper Fractions to Mixed Numbers Lesson AB 2 Reducing Fractions Lesson AB 3 Comparing Fractions Topic B: Making Like Units Pictorially Lesson 3 Lesson 4 Lesson 5 Lesson 5A Mixed Numbers to Improper Fractions Lesson 6 Lesson 7
Topic C: Making Like Units Numerically Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12
Topic D: Further Applications Lesson 13 Lesson 14 Lesson 15 Lesson 16 Word Problems
3
Module 3 – Introduction and Review Fractions with Number Lines Review What is a fraction ______________________________________________ _____________________________________________________________ What are the parts of a fraction?
5 6 What do the parts of the fraction tell us? Numerator _______________________________________________ Denominator ______________________________________________
Examples of Fractions :
______________________________________________ ______________________________________________ ______________________________________________ ______________________________________________ ______________________________________________ ______________________________________________ Draw
1 3
4 5
6 8
4
Plotting Fractions on number lines
If the numerator is less than the denominator the fraction is less than 1.
1 3
4 3
Add the numerator to make each fraction equal to 1 3
=1
Plot
3 6
2 Plot 5
6
=1
2
=1
8
=1
16
=1
5
6 Plot 8
Plot
1 4
Plot
2 5
Plot 1
2 5
6
Module 3 – Lesson 1 Equivalent Fractions with Number Lines Application Problem 15 kilograms of rice are separated equally into 4 containers. How many kilograms of rice are in each container? Express your answer as a decimal and as a fraction.
Simplify or Solve 3x4+6÷2
3 x (4 + 6) ÷ 2
207 x 124
7
Equivalent Fractions On the number line plot
1 2
and
3 6
1 2
3 6
On the number line plot
1 3
and
2 6
1 3
1 1 x = 3 3 x
2 6
=
2 6
How can you make an equivalent fraction?
____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________
8
Problem Set Make Equivalent fractions for the fractions below and plot them on a number line.
1 1 x = 4 4 x
=
2 2 x = 3 3 x
=
Using the same process make equivalent fractions for the fractions below.
4 7
1 8
2 5
7 9
9 10
3 7
1 14
9 11
9
Homework Make Equivalent fractions for the fractions below and plot them on a number line.
3 3 x = 4 4 x
=
1 1 x = 3 3 x
=
Using the same process make equivalent fractions for the fractions below.
4 5
1 8
2 5
7 9
9 10
3 7
1 14
9 11
10
Lesson 2 Equivalent Fractions with the Sums of Fractions with Like Denominators Application Problem Mr. Hopkins has a 1 meter wire he is using to make clocks. Each fourth meter is marked off with 5 smaller equal lengths. If Mr. Hopkins bends the wire at
¾ meter, what fraction of the marks is that?
Try solving using a number line or a tape diagram
Write in standard form and solve Three times the difference between 6 seventeens and 4 twenty fours
Solve
2.34 x 17 =
11
On the number line, mark the end points as zero and 1. Between zero and 1 estimate to make three parts of equal length and label them with their fractional value.
On your number line, show one third plus on third with arrows designating lengths.
The answer is
Express this as a multiplication equation and as an addition sentence.
Following the same pattern of adding unit fractions by joining lengths, show 3 fourths on a new number line. (Add two fractions to equal ¾)
Write the addition sentence.
12
On a number line, again mark the end points as zero and one. Between zero and one, estimate to make 8 parts of equal length. This time only label what is necessary to show 3 eighths. Represent 3 eighths + 3 eighths + 1 eighth on your number line. The answer is Express this as a multiplication equation and as an addition equation. On a number line, mark the end points as 0 halves and 6 halves below the number line. Estimate to make 6 parts of equal length. This time only label 2 halves. Record the whole number equivalents above the line. Represent 3 x 2 halves on your number line. The answer is Express this as an addition equation and as an multiplication equation.
13
Use a number line. Mark the end points as 0 fifths and 10 fifths below it. Estimate and give a value to the halfway point. What will be the value of the halfway point? Make 10 parts of equal length from 0 fifths to 10 fifths. Record the whole number equivalents above the line. Label 8 fifths on your number line. Show 8 fifths as the sum of 5 fifths and 3 fifths on your number line. Express this as an addition equation in two ways: as the sum of fifths and as the sum of a whole number and fifths. 8 fifths is between what 2 whole numbers?
14
Use a number line. Mark the end points as 0 thirds and 9 thirds below the number line. Divide the whole length into three equal smaller lengths and mark their values using thirds. What are the values of those points? Mark the whole number equivalents above the line. Divide each of those whole number lengths into three smaller lengths. Mark the number 7 thirds. Show 7 thirds as two units of 3 thirds and one more third on your number line and in an equation. 7 thirds is between what two whole numbers?
15
Express each fraction as the sum of two or three equal fractional parts. Rewrite each as a multiplication equation.
6 8
6 2 2 2 8 = 8 +8 +8
=
3 3 + 8 8
12 14
15 20
or
9 10
3 4
16
Lesson 2 Problem Set 1. Show each expression on a number line. Solve. a)
c)
b)
d)
x
2) Express each fraction as the sum of two or three equal fractional parts. Rewrite each as a multiplication equation.
6 a)
c)
9
b)
12 10
d)
7
2
27 5
17
3) Express each of the following as the sum of a whole number and a fraction.
4) Marisela cut four equivalent lengths of ribbon. Each was 5 eighths of a yard long. How many yards of fabric did she cut? Express your answer as the sum of a whole number and the remaining fractional units. Draw a number line to represent the problem.
18
Lesson 2 Homework 1) Show each expression on a number line. Solve. 1)
x
2) Express each fraction as the sum of two or three equal fractional parts. Rewrite each as a multiplication equation. a) b)
19 c)
d)
3) Express each of the following as the sum of a whole number and a fraction. a) b)
c)
d)
4) Natalie sawed five boards of equal length to make a stool. Each was 9 tenths of a meter long. How many meters of board did she saw? Express your answer as the sum of a whole number and the remaining fractional units. Draw a number line to represent the problem.
20
Improper Fractions to Mixed Numbers
Divide into fifths and plot
Plot
17 now write it as a whole number and a fraction 5
10 then write it as a whole number and a fraction 4
Converting improper fractions to mixed numbers strategy.
17 5 First divide the numerator by the denominator
3
3
The 3 is your whole number. While the remainder becomes the numerator.
Your denominator stays the same. Here is your mixed number
17 ÷ 5 = 3 r 2
17 2
13 2
79 9
21
35 4
37 5
13 7
5 2
28 3
25 3
65 7
32 6
36 5
64 7
12 7
42 5
22
78 9
66 7
68 8
3 2
19 3
38 4
23
Improper Fractions to Mixed Numbers Homework
17 5 First divide the numerator by the denominator
3
3
The 3 is your whole number. While the remainder becomes the numerator.
Your denominator stays the same. Here is your mixed number
17 ÷ 5 = 3 r 2
37 5
61 7
48 7
32 5
55 7
18 4
13 2
19 2
24 9
24
55 6
8 7
9 4
5 3
17 4
42 4
13 3
74 8
11 2
52 7
16 3
39 8
25
Divisibility Rules 2 – A number is divisible by 2 if it is even 3 – A number is divisible by 3 if the sum of its digits is divisible by 3 Example – 93 9 + 3 = 12 12 is divisible by 3 so 93 is divisible by 3 4 – A number is divisible by 4 if the last 2 digits are divisible by 4 Example – 724 24 is divisible by 4 so 724 is divisible by 4 5 – A number is divisible by 5 if it ends in a 5 or a 0 6 – A number is divisible by 6 if it is divisible by both 2 and 3 10 – A number is divisible by 10 if it ends in a 0 Reducing Fractions Greatest Common Factor
12
and 18
8
and
16
26
10
and
30
6
and
15
Find the greatest common factor of the numerator and the denominator
3 9
14 21
4 8
Use the Greatest common factor to reduce Each Fraction as Much as Possible
9 3 = 3 12
X X
3 3 = 4 4
Or
27
10 40
8 64
40 64
50 60
18 27
3 24
8 12
30 80
8 48
40 48
16 24
24 32
21 28
21 56
9 36
35 42
6 48
20 30
28
Reducing Fractions Homework Reduce Each Fraction as Much as Possible
5 40
4 16
5 20
6 9
2 4
2 16
24 32
3 6
8 12
15 24
21 56
10 60
49 56
7 56
3 12
5 15
9 72
15 18
29
Least Common Multiple and Comparing Fractions
30
Comparing Fractions
31
Comparing fractions on number lines Plot one fraction on each Number line and then compare.
32
Cross multiplying to compare
33
Problem Set
34
35
36
37
Lesson 3 Adding Fractions with Unlike Units by Making Equal Fractions Application Problem Alex squeezed 2 liters of juice for breakfast. If he pours the juice equally into 5 glasses, how many liters of juice will be in each glass? (Bonus: How many milliliters are in each glass?)
Solve – Use Decimals 216 ÷ 90 =
643 ÷ 80 =
38
Adding Fractions
2 4 8 + 8 =
What has to be the same in order to add two fractions? _____________________
4 8
+
1 8
=
1 6
+
4 6
=
How can you add two fractions with different denominators? ???? 1 4 + 8 6 Can we change a denominator in a fraction??? When???? Can we find an equivalent fraction for 4/8 and 1/6 that both fractions have the same denominator? Find the Least Common Multiple for 8 and 6 to help you find equivalent fractions with common denominators. Least Common Multiples 8 6 8 16 24 32 40 48 6 12 18 24 30 36 42 48 Which is the lowest one they have in common? There’s the denominator to use!!!
39
Make and equivalent fraction for 4/8 and 1/6 so both fractions have 24 as a denominator. 1 4 6 8 How to make equivalent fractions reminder Now you can add the fractions
.
Adding fractions Step 1 – rewrite vertically Step 2 – find the least common multiple for both denominators Step 3 – make an equivalent fractions using the new common denominator Step 4 – add the numerators
40
Adding fractions Step 1 – rewrite vertically Step 2 – find the least common multiple for both denominators Step 3 – make an equivalent fractions using the new common denominator Step 4 – add the numerators
41
Lesson 3 Problem Set 1) For the following problems, find common denominators and solve – simplify your answers.
a..
b.
c. d.
42
e. f.
Solve the following problems. Draw a picture and/or write the number sentence that proves the answer. Simplify your answer. Jamal used 1/3 yard of ribbon to tie a package and 1/6 yard of ribbon to tie a bow. How many yards of ribbon did Jamal use?
43
Over the weekend, Nolan drank 1/6 quart of orange juice, and Andrea drank 3/4 quart of orange juice. How many quarts did they drink together? Nadia spent 1/4 of her money on a shirt and 2/5 of her money on new shoes. What fraction of Nadia’s money has been spent? What fraction of her money is left?
44
Lesson 3 Homework 1) For the following problems, draw a picture using the rectangular fraction model and write the answer. Simplify your answer. a)
b)
c)
d)
45 e)
f)
Solve the following problems. Draw a picture and/or write the number sentence that proves the answer. Rajesh jogged 3/4 mile, and then walked 1/6 mile to cool down. How far did he travel?
46
Cynthia completed 2/3 of the items on her to‐do list in the morning, and finished
1/8 of the items during her lunch break. How much of her to‐do list is finished by the end of her lunch break? (Bonus: How much of her to‐do list does she still have to do after lunch?) Sam read 2/5 of her book over the weekend, and 1/6 of it on Monday. What fraction of the book has she read? What fraction of the book is left?
47
Lesson 4 Add Fractions with Sums Between 1 and 2 Application Problem Leslie has 1 liter of milk in her fridge to drink today. She drank 1/2 liter of milk for breakfast and 2/5 liter of milk for dinner. How many liters did Leslie drink during breakfast and dinner?
(Bonus: How much milk does Leslie have left over to go with her dessert, a brownie? Give your answer as a fraction of liters and as a decimal.)
Simplify 183 – 3 x 50 – (2 + 6)
[56 ÷ (11 – 3)] + 3 3
48
1 1 When you see this problem, can you estimate the answer? 3 4 Will it be more or less than 1? Now look at this problem. Estimate the answer. 1 3 4 2 Will it be more or less than 1? What stops us from simply adding?
Find common denominators and then writing the new equation.
What is unusual about the answer?
49
Solve
4 + 1 5 2
Solve
2 + 3 3 5
Solve
3 + 2 8 3
50
Lesson 4 Problem Set For the following problems, find common denominators and write the answer. When possible, write your answer as a mixed number. a. b.
c.
d.
51
e.
f.
Solve the following problems. Draw a picture and/or write the number sentence that proves the answer. Simplify your answer. Penny used 2/5 lb of flour to bake a vanilla cake. She used another 3/4 lb of flour to bake a chocolate cake. How much flour did she use altogether?
52
Carlos wants to practice piano 2 hours each day. He practices piano for 3/4 hour before school and 7/10 hour when he gets home. How many hours has Carlos practiced piano? How much longer does he need to practice before going to bed in order to meet his goal?
53
Lesson 4 Homework Directions: For the following problems, draw a picture using the rectangular fraction model and write the answer. When possible, write your answer as a mixed number. a. b.
c.
d.
54
e.
f.
Solve the following problems. Draw a picture and/or write the number sentence that proves the answer. Simplify your answer. Sam made 2/3 liter of punch and 3/4 liter of tea to take to a party. How many liters of beverages did Sam bring to the party?
55
Mr. Sinofsky used 5/8 of a tank of gas on a trip to visit relatives for the weekend and another half of a tank commuting to work the next week. He then took another weekend trip and used 1/4 tank of gas. How many tanks of gas did Mr. Sinofsky use altogether?
56
Lesson 5 Subtract Fractions with Unlike Units by Using Equivalent Fractions Application Problem A farmer uses 3/4 of his field to plant corn, 1/6 of his field to plant beans , and the rest to plant wheat. What fraction of his field is used for wheat?
Estimate and then solve for actually amount 2307 x 452
782 x 122
57
Can we subtract this? Explain.
3 - 2 = 5 5
Can we subtract this? Explain.
1 - 1 = 3 4
1 - 1 = 2 5
2 - 1 = 3 4
58
1 - 2 = 2 7
4 - 2 = 5 3
59
Lesson 5 Problem Set For the following problems, find common denominators and write the answer. Simplify your answer. a. b.
c.
d.
60
e.
f.
Mr. Penman had 2/3 liter of salt water. He used 1/5 of a liter for an experiment. How much salt water does Mr. Penman have left?
61
Sandra says that because all you have to do is subtract the numerators and subtract the denominators. Convince Sandra that she is wrong. You may draw a rectangular fraction model to help.
62
Lesson 5 Homework 1) Find common denominator and subtract.
2) Find the difference. Convert to fractions with common denominators. a.
b.
c.
d.
63
e.
f.
Robin used 1/4 pound of butter to make a cake. Afterward she had 5/8 of a pound left. How much butter did she have at first?
Katrina needs 3/5 kilogram of flour for a recipe. Her mother has 3/7 kilogram in her pantry. Is this enough flour to make the recipe If not, how much more will she need?
64
Mixed Numbers to Improper Fractions
2 1/6 0
Plot on the number line
1
How many 6ths all together?
2
3
2
3
2
3
_____
6 1 5/8 0
Plot on the number line
1
How many 8ths all together?
_____
8 2 2/4 0
Plot on the number line
1
How many 4ths all together?
_____
4
65
Strategy First multiply the denominator times the whole number.
1
2 /6 6 × 2 = 12 Next, add your answer from step 1 to your numerator. 12 + 1 = 13 Keep your denominator the same 13 6 _____________________________________________________________
1 5/8
2 2/4
denominator x whole number Add answer to the numerator Keep denominator the same
2 6
1 7
2 5
66
1 8
1 6
4 6
4 6
6 7
2 5
2 10
1 9
1 3
67
4 6
1 2
2 4
2 8
2 3
1 7
68
Mixed Numbers to Improper Fractions Homework
Mixed Numbers to Improper Fractions
2 5
First multiply the denominator times the whole number. 5 × 3 = 15 Next, add your answer from step 1 to your numerator. 15 + 2 = 17 Keep your denominator the same
17 5 _____________________________________________________________
1 4
6 9
5 8
5 8
6 7
1 2
69
4 8
4 6
3 10
8 9
8 9
6 9
1 4
1 2
8 9
4 6
5 6
6 9
70
Lesson 6 – Subtract Fractions from numbers between 1 and 2 Application Problem The Napoli family combined two bags of dry cat food in a plastic container. One bag had 5/6 kg. The other bag had 3/4 kg. What was the total weight of the container after the bags were combined?
Solve 104.35 x 34 =
480,000 ÷ 600 =
71
- Convert mixed number to improper fraction - Find common denominator - Solve - Simplify
1 1 1 3 2
1 1 1 5 3
72
3 4 1 4 5
4 1 1 9 2
73
Lesson 6 Problem Set
Convert mixed number to improper fraction - Find common denominator – Solve - Simplify a.
b.
c.
d.
74
e.
f.
1. Jean‐Luc jogged around the lake in 1 1/4 hour. William jogged the same distance in 5/6 hour. How much longer did Jean‐Luc take than William in hours? How many more minutes? 2. Is it true that ? Prove your answer.
75
Lesson 6 Homework 1.
a.
Find the difference. Use a rectangular fraction model to show how to convert to fractions with common denominators. b.
c.
d.
76
e.
f.
g.
h.
77
2.
Sam had 1 1/2 m of rope. He cut off 5/8 m and used it for a project. How much rope does Sam have left?
3.
Jackson had 1 3/8 kg of fertilizer. He used some to fertilize a flower bed and he only had 2/3 kg left. How much fertilizer was used in the flower bed?
78
Lesson 7 – Two Step Word Problems Lesson 7 Problem Set George weeded 1/5 of the garden, and Summer weeded some, too. When they were finished, 2/3 of the garden still needed to be weeded. What fraction of the garden did Summer weed?
Jing spent 1/3 of her money on a pack of pens, 1/2 of her money on a pack of markers, and 1/8 of her money on a pack of pencils. What fraction of her money is left?
79
Shelby bought a 2 ounce tube of blue paint. She used 2/3 ounce to paint the water, 3/5 ounce to paint the sky, and some to paint a flag. After that she has 2/15 ounce left. How much paint did Shelby use to paint her flag?
Jim sold 3/4 gallon of lemonade. Dwight sold some lemonade too.
Together, they sold 1 5/12 gallons. Who sold more lemonade, Jim or Dwight? How much more?
Leonard spent 1/4 of his money on a sandwich. He spent 2 times as much on a gift for his brother as on some comic books. He had 3/8 of his money left. What fraction of his money did he spend on the comic books?
80
Lesson 7 Homework Christine baked a pumpkin pie. She ate 1/6 of the pie. Her brother ate 1/3 of it, and gave the left overs to his friends. What fraction of the pie did he give to his friends?
Liang went to the bookstore. He spent 1/3 of his money on a pen and 4/7 of it on books. What fraction of his money did he have left?
Tiffany bought 2/5 kg of cherries. Linda bought 1/10 kg of cherries less than Tiffany. How many kg of cherries did they buy altogether?
81
Mr. Rivas bought a can of paint. He used 3/8 of it to paint a book shelf. He used 1/4 of it to paint a wagon. He used some of it to paint a bird house, and have 1/8 of paint left. How much paint did he use for the bird house?
Ribbon A is 1/3 m long. It is 2/5 m shorter than ribbon B. What’s the total length of two ribbons?
82
Fraction Practice In order to Add, Subtract, or compare fractions what do they have to have? ____________________________________________________ What is a fraction that has a larger numerator than denominator called? ____________________________________________________ A whole number that is followed by a fraction is called? _____________________ Make an equivalent fraction Make each fraction equal 1 4 =1 =1 7 8 16 Express each fraction as the sum of 1 two or three equal fractional parts. 8 Rewrite each as a multiplication equation. 2 6 2 2 2 3 3 6 = + or = + + 5 8 8 8 8 8 8 8 7 12 9 15 Convert to improper fractions
8 10 4 6
1 5
1 6
83
Convert to mixed numbers
32 5
55 7
18 4
Reduce
40 48
16 24
24 32
84
Lessons 9 and 10 – Adding and Subtracting Fractions Application Problem Hannah and her friend are training to run in a 2 mile race. On Monday, Hannah runs 1/2 mile. On Tuesday, she runs 1/5 mile further than she ran on Monday. How far did Hannah run on Tuesday?
If her friend ran 3/4 mile on Tuesday, how many miles did the girls run in all on Tuesday?
85
Sam and Nathan are training for a race. Monday, Sam ran 2 3/4 miles, and Nathan ran 2 1/3 miles. How much farther did Sam run than Nathan?
86
Lessons 9 and 10 Problem Set Solve and Simplify
87
88
89
Whitney says that to add fractions with different denominators, you always have to multiply the denominators to find the common unit, for example: Show Whitney how she could have chosen a denominator smaller than 24, and solve the problem. Jackie brought of a gallon of iced tea to the party. Bill brought of a gallon of iced tea to the same party. How much iced tea did Jackie and Bill bring to the party?
90
Madame Curie made some radium in her lab. She used kg of the radium in an experiment and had kg left. How much radium did she have at first? (Bonus: If she performed the experiment twice, how much radium would she have left?)
Erin jogged miles on Monday. Wednesday she jogged miles, and on Friday she jogged miles. How far did Erin jog altogether?
91
Darren bought some paint. He used gallons painting his living room. After that, he had gallons left. How much paint did he buy? Clayton says that will be more than 5 but less than 6 since 2 + 3 is 5. Is Clayton’s reasoning correct? Prove him right or wrong.
92
Lessons 9 and 10 Homework Make like units, then add. Use an equation to show your thinking.
93
Add.
94
95
On Monday, Ka practices guitar for 2/3 of one hour. When she’s finished, she practices piano for ¾ of one hour. How much time did Ka spend practicing instruments on Monday?
96
Ms. How buys a bag of rice to cook dinner. She used 3/5 kg of rice and still had 2 and ¼ kg left. How heavy was the bag of rice that Ms. How bought?
Joe spends 2/5 of his money on a jacket and 3/8 of his money on a shirt. He spends the rest on a pair of pants. What fraction of his money does he use to buy the pants?
97
Angela practiced piano for 2 ½ hours on Friday, 2 1/3 hours on Saturday, and 3 2/3 hours on Sunday. How much time did Angela practice piano during the weekend?
String A is 3 5 /6 meters long. String B is 2 1/ 4 long. What’s the total length of both strings?
98
Lessons 11 and 12 Adding and Subtracting Fractions Application Problem Meredith went to the movies. She spent 2/5 of her money on a ticket and 3/7 of her money on popcorn. How much of her money did she spend? (Bonus: How much of her money is left?) Max’s reading assignment was to read 15 1/2 pages. After reading 4 1/3 pages, he took a break. How many more pages does he need to read to finish his assignment?
99
To make punch for the class party, Mrs. Lui mixed 1 1/3 cups orange juice, 3/4 cup apple juice, 2/3 cup cranberry juice, and 3/4 cup lemonlime soda. Mixed together, how many cups of punch does the recipe make? (Bonus: Each student drinks 1 cup. How many recipes does Mrs. Lui need to serve her 20 students?)
100
101
Lessons 11 and 12 Problem Set Generate equivalent fractions to get the same unit, then subtract.
102
103
Subtract.
104
George says that to subtract fractions with different denominators, you always have to multiply the denominators to find the common unit, for example: Show George how he could have chosen a denominator smaller than 48, and solve the problem.
Meiling has liter of orange juice. She drinks liter. How much orange juice does she have left? (Bonus: If her brother then drinks twice as much as Meiling, how much is left?)
105
Harlan used
kg of sand to make a large hourglass. To make a small hourglass
he only used kg of sand. How much more sand does it take to make the large hourglass than the small one? Toby wrote the following: Is Toby’s calculation correct? Draw a diagram to support your answer.
106
Mr. Neville Iceguy mixed up gallons of chili for a party. If gallons of chili was mild, and the rest was extra spicy, how much extra spicy chili did Mr. N. Iceguy make? Jazmyne determined to spent
hours studying over the weekend. She spent
hours studying on Friday evening and
hours on Saturday. How much
longer does she need to spend studying on Sunday in order to reach her goal?
107
Lessons 11 and 12 Homework First find a common unit, then subtract.
108
109
Subtract.
110
111
Sandy ate of a candy bar. John ate of it. How much more of the candy bar did John eat than Sandy? yards of cloth are needed to make a woman’s dress. yards of cloth are needed to make a girl’s dress. How much more cloth is needed to make a woman’s dress than a girl’s dress?
112
Bill reads of a book on Monday. He reads of the book on Tuesday. If he finishes reading the book on Wednesday, what fraction of the book did he read on Wednesday? Tank A has a capacity of 9.5 gallons. gallons of the tank’s water are poured out. How much water is left in the tank?
113
Tony wrote the following: Is Tony’s statement correct? Explain. Ms. Sanger blended there were she use?
gallons of iced tea with some lemonade for a picnic. If gallons in the mixture, how many gallons of lemonade did
114
A carpenter has a
foot wood plank. He cuts off
feet to replace the slat
of a deck and feet to repair a bannister. He uses the rest of the plank to fix a stair. How many feet of wood does the carpenter use to fix the stair?
115
Lesson 13 – Fraction Benchmarks to Check Reasonableness Application Problem Mark jogged 3 5/7 km. His sister jogged 2 4/5 km. How much farther did Mark jog than his sister?
Solve: 62 x 100 =
282 x 42 =
26.72 x 100 =
240 x 2000 =
116
1 + 3 2 4 Without calculating what can you tell me about the value of this expression?
2 2 1 5 ‐ 3 Without calculating what can you tell me about the value of this expression?
4 10
+
1 3
Without calculating what can you tell me about the value of this expression?
4 10
+
2 9
Without calculating what can you tell me about the value of this expression?
117
4 9 1 7 ‐ 10 Without calculating what can you tell me about the value of this expression?
4 5
-
1 8
Without calculating what can you tell me about the value of this expression?
Use > , , ,
